Skip-counting stories

Learning Objectives Identify whether a story problem represents an arithmetic or geometric sequence. Determine the initial term (a_1), common difference (d), or common ratio (r) from a word problem. Write an explicit formula for an arithmetic or geometric sequence that models a real-world scenario. Use the explicit formula to calculate the value of a specific term (a_n) in a sequence. Solve for the term number (n) when given the value of a term in a linear context. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions. Translate a narrative into a mathematical model representing a sequence. If you saved $10 in January and doubled your savings each month, how much would you save in December? 🤯 Let's find out without adding i...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.The list 3, 7, 11, 15, ... is a sequence where each term is 4 more than the previous one. Arithmetic SequenceA sequence where the difference between consecutive terms is constant. This is like skip-counting by adding or subtracting the same number each time.A stack of cans with 10 on the bottom row, 9 on the next, 8 on the one above, and so on. The sequence is 10, 9, 8, ... and the constant difference is -1. Common Difference (d)The constant value added to each term to get the next term in an arithmetic sequence.In the sequence 5, 12, 19, 26, ..., the common difference is d = 7. Geometric SequenceA sequence where the ratio between consecutive terms is constant. This is like skip-...

Explicit Formula for an Arithmetic Sequence a_n = a_1 + (n-1)d Use this formula to find the value of any term ('a_n') in an arithmetic sequence if you know the first term ('a_1'), the term's position ('n'), and the common difference ('d'). It's a direct link to the linear function y = mx + b. Explicit Formula for a Geometric Sequence a_n = a_1 * r^(n-1) Use this formula to find the value of any term ('a_n') in a geometric sequence if you know the first term ('a_1'), the term's position ('n'), and the common ratio ('r'). This is directly related to exponential functions of the form y = ab^x.